Questions

  1. How do species differ in their drought response to variable intensity and their recovery patterns?
  2. If species differ, do they also vary regionally? For which species?
  3. Are drought response and recovery mediated by competition and tree size and is this a species specific phenomenon or does it also vary regionally?

Methods

I collected tree ring data from 4 regions across California and performed analyses on detrended growth during drought years where water availability (SPEI) was in the bottom 10th percentile. All tree ring series were spline detrended.

Key responses

\[ Growth Reduction = \frac{\overline{RWI}_{non-drought} - RWI_{drought}}{\overline{RWI}_{non-drought}} \] \[ Recovery = RWI_{actual} - RWI_{pred} \]

Where \(RWI_{pred}\) is the predicted growth for a tree given the post-drought year conditions based on hierarchical Bayesian models of all growth years.

Full model approach to Q3

This approach differs in that here we explore the results of the full expression of the model to answer the above questions i.e. the most complex justifiable model. Each species is modeled independently. This approach is a way to avoid the model selection issues we discussed regarding the complexity of question 3.

\[ Reduction_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}SPEI_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}SPEI_i\times DBH_i + \beta_{5}SPEI_i \times BA_i \]

and for recovery:

\[ Recovery_i \sim Normal(\mu_i, \sigma_i) \]

\[ \mu_i = \alpha_{region_i} + \alpha_{treeID} + \beta_{1region_i}Reduction_i + \beta_{2}DBH_i + \beta_{3}BA_i + \beta_{4}Reduction_i\times DBH_i + \beta_{5}Reduction_i \times BA_i \]

Regionally varying responses to drought intensity or severity could reflect local adaptation.

Descriptions of interaction terms

\(SPEI \times DBH\) smaller or larger trees experience the same drought intensity differently. Perhaps this is due to differences in evaporative demand, root:shoot allocation patterns, height water relationship

\(Reduction \times DBH\) smaller or larger trees recover from equally damaging droughts differently. Potentially due to access to resources, allocation again.

\(SPEI \times BA\) sparse or dense neighborhoods modify the effect of drought intensity. This could be via resource (water) competition. Although because we lack good characterization of the between neighborhood microsite differences density could reflect suitability more than competition.

\(Reduction \times BA\) sparse or dense neighborhoods modify the recovery of trees from equally damaging droughts. This could also be via resource competition although more than just water. Again, patterns may reflect uncharacterized microsite differences rather than competition.

Details

All models converged Rhat ~1 and each model had few divergent samples. Param estimates and plots were prepared with tidybayes. Marginal effects plots were produced with add_fitted_draws() .

Results

Q1 Species differences

Growth Reduction

Table SX. Growth reduction WAIC table
waic_diff se
SPEI only 0.00 0.00
Species + SPEI 1.78 3.06
Species * SPEI 3.86 3.71
Table SX. Growth reduction WAIC table variance term
waic_diff se
Species var 0.00 0.00
Global var 46.08 15.61
Table SX. Growth reduction variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0678695 0.0095051 0.0524760 0.0835043 Inf 1.00000
PL - AC > 0 0.0356420 0.0115867 0.0161894 0.0539996 1332.3333333 0.99925
PL - PJ > 0 -0.1274074 0.0467587 -0.2027858 -0.0502629 0.0025063 0.00250
Table SX. Growth reduction intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0203995 0.0129695 -0.0006292 0.0417334 16.7777778 0.94375
PL - AC > 0 0.0101130 0.0163853 -0.0170997 0.0375752 2.7313433 0.73200
PL - PJ > 0 -0.0102865 0.0164266 -0.0374510 0.0168000 0.3633265 0.26650

Recovery

Table SX. Recovery WAIC table
waic_diff se
Varying intercept and slope 0.00 0.00
Varying intercept 5.51 9.90
No species effect 12.47 11.84
Table SX. Recovery WAIC table, variance term
waic_diff se
Species var 0.00 0.0
Global var 33.67 20.2
Table SX. Recovery variance contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0555744 0.0085943 0.0411071 0.0695725 Inf 1.00000
PL - AC > 0 0.0359705 0.0108185 0.0188759 0.0544338 3.99900e+03 0.99975
PL - PJ > 0 -0.0902395 0.0498857 -0.1706638 -0.0067311 4.00416e-02 0.03850
Table SX. Recovery intercept contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 0.0314717 0.0178364 0.0018100 0.0604578 25.31579 0.96200
PL - AC > 0 0.0965939 0.0213785 0.0609767 0.1319395 Inf 1.00000
PL - PJ > 0 0.0651223 0.0216478 0.0292203 0.1005338 3999.00000 0.99975
Table SX. Recovery slope contrasts
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
PJ - AC > 0 -0.0767700 0.0413998 -0.1449606 -0.0097026 0.0309278 0.03000
PL - AC > 0 0.0820008 0.0527384 -0.0049174 0.1673384 15.7364017 0.94025
PL - PJ > 0 0.1587708 0.0505887 0.0746240 0.2418538 570.4285714 0.99825

Param Plots

Main Figure

Q2 Regional Differences

Growth Reduction

Table SX. A. concolor growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
No regional effects 43.30953 12.80732
Varying intercept 45.11601 12.72891
Table SX. P. jeffreyi growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.00000
Varying intercept 41.83552 12.88420
No regional effects 43.82051 13.91644
Table SX. P. lambertiana growth reduction WAIC table
waic_diff se
Varying intercept and slope 0.00000 0.000000
No regional effects 18.41681 7.836080
Varying intercept 19.29546 7.449942 
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.69  CI 95%: [0.48 0.81]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.08  CI 95%: [0.06 0.15]
## Conditioned on rand. effects: 0.26  CI 95%: [0.16 0.41]
## 
## ## Difference in Variances
## Difference: 0.18  CI 95%: [0.08 0.31]
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.59  CI 95%: [0.36 0.73]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.11  CI 95%: [0.09 0.16]
## Conditioned on rand. effects: 0.27  CI 95%: [0.17 0.42]
## 
## ## Difference in Variances
## Difference: 0.16  CI 95%: [0.06 0.30]
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.34  CI 95%: [-0.01 0.65]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.11  CI 95%: [0.07 5.67]
## Conditioned on rand. effects: 0.21  CI 95%: [0.11 5.76]
## 
## ## Difference in Variances
## Difference: 0.08  CI 95%: [-0.03 0.20]

Recovery

Table SX. A. concolor recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 1.851447 5.964911
No regional effects 12.912958 9.351119
Table SX. P. jeffreyi recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 7.988191 8.352711
No regional effects 22.441717 12.987328
Table SX. P. lambertiana recovery WAIC table
waic_diff se
Varying intercept and slope 0.000000 0.000000
Varying intercept 4.836886 8.154183
No regional effects 36.244175 11.872226 
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.05  CI 95%: [-0.09 0.19]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.06  CI 95%: [0.05 0.09]
## Conditioned on rand. effects: 0.06  CI 95%: [0.05 0.09]
## 
## ## Difference in Variances
## Difference: 0.00  CI 95%: [-0.01 0.01]
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.03  CI 95%: [-0.09 0.14]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.10  CI 95%: [0.08 0.17]
## Conditioned on rand. effects: 0.10  CI 95%: [0.08 0.17]
## 
## ## Difference in Variances
## Difference: 0.00  CI 95%: [-0.01 0.02]
## # Random Effect Variances and ICC
## 
## Conditioned on: ~(1 | Region)
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.04  CI 95%: [-0.15 0.20]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.08  CI 95%: [0.06 0.65]
## Conditioned on rand. effects: 0.08  CI 95%: [0.06 0.64]
## 
## ## Difference in Variances
## Difference: 0.00  CI 95%: [-0.02 0.02]

Param Plots

Main Figure

Q3

Param Plots

Main Figure

Growth Reduction

Keep in mind that in the scatter plots the drought intensity axis is flipped, so slope will appear to be wrong sign from the parameter estimate plots.

Recovery